We study the membership problem for regular expressions extended with operators for unordered concatenation and numerical constraints. The unordered concatenation of a set of regular expressions denotes all sequences consisting of exactly one word denoted by each of the expressions. Numerical constraints are an extension of regular expressions used in many applications, e.g. text search (e.g., ...

Note that a phrase headed by -te (teP) is usually an adjunct floating around in a sentence (like English gerunds); however, when V-te is adjacent to a verb from a certain set of verbs, they jointly form a single complex predicate. The status of a [V-te V] string as a complex predicate (rather than two separate predicates) is clear when the semantics of V2 is significantly lightened, but even if...

In the seventies, several classification schemes for the rational languages were proposed, based on the alternate use of certain operators (union, complementation, product and star). Some thirty years later, although much progress has been done, several of the original problems are still open. Furthermore, their significance has grown considerably over the years, on account of the successive di...